Overlap integrals: What are they and how do we arrive at the formula?

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SUMMARY

The discussion centers on overlap integrals, which quantify the interaction between electron densities of two atomic orbitals. Specifically, the overlap integral measures how much the electron density of one nucleus overlaps with that of another. The formula for overlap integrals is derived from the linear combination of atomic orbitals (LCAO) method, which is fundamental in molecular orbital theory. Understanding these concepts is crucial for analyzing molecular interactions in quantum chemistry.

PREREQUISITES
  • Linear Combination of Atomic Orbitals (LCAO)
  • Quantum Chemistry Fundamentals
  • Atomic Orbitals and Molecular Orbitals
  • Basic Understanding of Electron Density
NEXT STEPS
  • Study the derivation of the overlap integral formula in quantum chemistry
  • Explore the implications of overlap integrals in molecular orbital theory
  • Learn about the role of basis sets in quantum mechanical calculations
  • Investigate computational tools for calculating overlap integrals, such as Gaussian or GAMESS
USEFUL FOR

Students and professionals in quantum chemistry, computational chemists, and anyone interested in molecular interactions and orbital theory will benefit from this discussion.

Mazzur
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Hey I've been looking all over the web and I can't find any comprehensible information on overlap integrals. What does the overlap integral of two functions give us? And why?

Thanks in advance!
 
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hint: change of basis
 
ansgar said:
hint: change of basis

lol sorry - I don't have a clue what the basis even refers to...
 
Mazzur said:
lol sorry - I don't have a clue what the basis even refers to...

Basis(basis set) = atomic orbitals from which the MO is built.
So overlap integrals is a measure of the interracton between a nucleus and electron density centred on the other nucleus . Note that this is just partial example of what overlap integral is.
I guess we arrive at the formula by considering the fact that atomic orbitals can be combined linearly.
 

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